Question

Image text transcribed for accessibility:Two short term radioactive hazards from the detonation of a nuclear weapon are 38Sr92 and 39Y92. Radioactive Strontium 92 decays to Yterbium 92 which in turn decays to stable Zirconium 92. 38Sr92 has a half life of 2.8 hours, and 39Y92 has a half life of 3.5 hours. Each decays according to the exponential decay model, but it's more complicated because the Yterbium is replenished by the decay of the Strontium. It's still an exponential problem. If we start with 100 grams of Strontium 92, the decay of that element has a constant k for Sr(t) = 100g e - ksr t. If we started with just 100g of Y92 then Y(t) = 100g e - ky t. For both, use x(t) = e - At x(0) where x(0) is the initial mix of the elements. Use 100g, 0, and 0 for Sr, Y, and Zr respectively. The matrix A is below. We want the number of grams of each remaining at t = 8 hours (a full work day with no lunch). A = Solve with X=expm( - A * t) * X0. (You will need to find kSr, kY first.) answer: Sr(8 hours) = Y(8 hours) = Zr(8 hours) =